The “digital engineering” of the present invention specially refers to “digital computation systematic engineering”. It relates to the technical solution of realizing the digital engineering of the computation system per se like four arithmetic operations principle. “Numerical calculations that use tools” include written calculation, abacus calculation, mechanical calculation, electrical calculation, and count calculation, etc. in history. Nowadays, only digital electrical calculation, abacus calculation, and written calculation remain, so the corresponding digital calculation systematic engineering includes only three kinds, which are digital computer, abacus, and numerical calculation systematic engineering that uses a pen and paper for written calculation, which is called “written calculation engineering” for short.
The four arithmetic operations in the current digital engineering method, first of all addition, are not quite satisfactory, the major deficiencies are that the speed of computation is slow and in subtraction, the negatives are not brought to their full play, meanwhile, successive subtraction cannot be done. Especially in the combined computations of addition and subtraction, the computations cannot be finished in a single step; in multiplication, the deficiencies of addition expand and become more serious; in division, the above-mentioned deficiencies exist, too. In summary, in the smallest mathematical entity—the rational number entity, the situation of the four arithmetic operations is not satisfactory.
In digital engineering of written calculation, dissection of the computation shows that some implicit computation procedures exist, thus causing some “hidden trouble”. Take addition of two numerals as an example, the formula thereof is as formula 1: 123456+345678=469134 [all the numerals in this text whose numerical system are not indicated are common decimal numerals, the same below], wherein the sum at the tens place is 3, and the micro-program operation is as follows in a dissection: {circle around (a)} a carry from the units place; {circle around (b)} the two tens places 5 and 7 are added to the carry of the lower place, i.e., (5+7+1), and the units place of the sum is taken; {circle around (c)} the carry of the sum of (5+7+1) is sent to the higher place, and the rest of the places have the similar situation. Another example is as example 2, wherein three numerals are to be added for the sum, and the formula thereof is as formula 2: 78+297+295=634. It can be seen that the above-mentioned deficiencies are more serious. It is obvious that the following deficiencies exist:
a. It is difficult to mark the carry. If numerals of smaller size are used to indicate the carry, it is liable to cause confusion and the area of the numeral is limited. In particular, the situation is more annoying when 456789 is to be represented, because if the “.” is written between the numerals, it is liable to be mixed up with a decimal, and it is inconvenient to represent 456789; if fingers are used to count the numbers, it is slow and inconvenient; if mental calculation is performed, it is a hard mental work and mistakes usually occur.b. Usually when two numerals are added, there will be three numerals at each place to be added for a sum, so there is the need for a three-layered computation, and when three or more numerals are to be added for a sum, it becomes more inconvenient.c. It is difficult to check the computations. The computation is usually performed once again, so it is time-consuming and labor-consuming.
Subtraction is more troublesome than addition, and “successive subtraction” within the same vertical formula is impossible, so it must be separated; especially in the combined computations of addition and subtraction, the computation cannot be finished in a single step. In multiplication, this problem is more serious, besides, the formats for the computations of addition, subtraction, multiplication and division are not uniform, and a different format is used for division.
On the other hand, in computer digital engineering, the numerals are usually represented by the common binary numerals, and the negatives are usually represented by the true form, the one's complement, the complement, and the frame shift, etc. In the current computers, computations are all carried out with two numerals, and “multiple computations” cannot be realized. The so-called “multiple computation” means that more than two numerals are added or subtracted at the same time. In the computers that adopt other common numerical systems like the common Q-ary, a lot of corresponding complexities exist [Q is a natural numeral].
Moreover, in digital engineering of abacus, the numerals are usually “combined Q-ary” numerals using common binary and common quinary. Therefore, the pithy formulae for the computations are miscellaneous and there are the corresponding complexities.